Question

# In chapter 3, it was noted that the mean is the most commonly used measure of...

In chapter 3, it was noted that the mean is the most commonly used measure of central tendency. Partly because variance and standard deviation are directly related to the mean, these two values are the most common measures of variability. Explain how variance and standard deviation are related to the mean.

Variance and standard deviation are both determined by the help of mean of a group of numbers in question(this group called sample or population). The mean is the average of the group and the variance measures the average degree to which each number is different from the mean in that group. The extent of the variance correlates to the size of the overall range of numbers—that is, the variance is greater when there is a wider range of numbers in this group, and the variance is less when there is a narrower range of numbers. the standard deviation is the square foot of variance.

the variance of a group which has n observations ( numbers) can be calculated as

if we find the variance of sampke zhen devide n-1 instead of n due to degree of freedom.